Stress Concentration at Notches

Calculations on the strength of structures are primarily based on the theory of elasticity. If the yield stress is exceeded plastic deformation occurs and the more complex theory of plasticity has to be used. Fatigue, however, and also stress corrosion, are phenomena which usually occur at relatively low stress levels, and elastic behavior may well be assumed to be applicable. The macroscopic elastic behavior of an isotropic material is characterized by three elastic constants, the elastic modulus or Young's modulus (E), shear modulus (G) and Poisson's ratio (ν). The well-known relation between the constants is E = 2G(1 + v).

In a structure, geometrical notches such as holes cannot be avoided. The notches are causing an inhomogeneous stress distribution, see Figure 3.1, with a stress concentration at the “root of the notch”. The (theoretical) stress concentration factor, K _t , ⁶ is defined as the ratio between the peak stress at the root of the notch and the nominal stress which would be present if a stress concentration did not occur.